This was one of the stories used in the film O. Henry's Full House (1952). In the original, two struggling young artists live in a tiny apartment in the Village that would probably go for $3700 a month these days. One is ill and has a fragile grasp on life for which her metaphor is the leaves of ivy on the wall as the winter wind takes them one by one. Hollywood turned the roommate into a little girl and the leaves of ivy became leaves on a tree and on and on.
The author's real name was Sidney Porter and he was a distant cousin of Katherine Anne Porter.
The text for this story may be found at www.gutenberg.org